Order Management System Proposal Using Inventory Balance Equation with Non-continuous Replenishment

Abstract

The purpose of this paper is to present an inventory balance model including an order-up-to replenishment policy with partial backlogging. Pictured in the model is a situation, where goods are not replenished continuously, but only at predetermined intervals. The model is described by ordinary differential equations with delayed argument because of the assumption of a time lag between ordering and delivery.
A computer simulation which helps to demonstrate and verify model behaviour is utilized for the numerical solution of the model. Sales data of a real company are used as the input data.
Due to the comparison of the designed model outputs against the real state in the company, it was verified that it is possible to achieve a substantial reduction in warehousing costs without a disproportionate increase in the risk of inventory shortage. The authors note that modern methods of functional analysis can be successfully applied in solving an inventory balance model.